for a collection of \(N\)  samples \((z^i)_{i=1}^N\)  from
\(\mathcal {N}({\bf 0}, {\bf I}_n)\)  and for some
approximation space \(\mathcal {H}\) .
There is an important difference between
(REF ) and (REF ):
the density \(\eta \)  in (REF ) is
always
log-concave, while \(\pi \)  in (REF ) need not be.
As a result,
(REF ) is in general not
a convex problem [1]}.
Moreover, we cannot compute
the components of \({\widehat{\mathcal {T}}}\)  independently as in
(REF ), since
\(\pi \)  need not factorize as a product of its marginals.
Hence, the computation of \({\widehat{\mathcal {T}}}\)  is
inherently harder than that of \({\widehat{S}}\) , but
still feasible. The numerical
solution of (REF ) in the
context of Bayesian inference was pioneered by
[2]},
which uses gradient-based optimization (e.g., BFGS or Newton-CG [3]}) to minimize
an equivalent reformulation of (REF ),
\( \widehat{\mathcal {T}} \in \arg \min _{U \in \mathcal {H}} \,- \frac{1}{N} \sum _{i=1}^N \,\left( \log \, \pi (U(z^i))+ \sum _{k=1}^n \log \partial _k U^k(z^i)\right), \) 
